Spintronics is a rapidly growing research field aimed at realizing new high performance (spintronic) devices that takes advantage of the electron spin as well as of its charge. One of the important requirements necessary in developing semiconductor spintronic devices is the efficient generation of spin-polarized charge carriers (or spin current) in a semiconductor, transporting them reliably over reasonable distances and then detecting them. An electrical means of detecting spin current in semiconductors is very desirable for fully exploring the possibility of utilizing spin degree of freedom and spintronic device applications. A more general drift-diffusion equation that takes into account electric-field effects and both nondegenerate (NDG) and degenerate (DG) electron statistics was derived. Using this drift-diffusion model, it was shown that the extension of the spin diffusion length by a strong electric-field does not result in a significant increase in spin current in semiconductors owing to the competing effect of the electric field on diffusion. It was found that there is a spin drift-diffusion crossover field (E ~) for a process in which the drift and diffusion contribute equally to the spin current. Expressions were derived that relate E ~ to the intrinsic spin diffusion length (D0) of a semiconductor for all electron statistical regimes. The anomalous Hall effect (AHE) arising from the spin current was also derived on the basis of the drift-diffusion model and a useful way was demonstrated for the electrical detection of spin current and spin diffusion length in a semiconductor. For the possible enhancement of the diffusive part, DG and NDG cases were considered. It was found that, owing to an increase in the diffusion coefficient, the spin current and hence the AHE increase in a DG semiconductor. Devices for the electrical detection of spin current, based on the AHE, were fabricated on undoped as well as on Si-doped GaAs using nonmagnetic contact materials, producing a successful grecipe h for growth and metallization. They were characterized as to their suitability for applications and were found to contain transparent contacts. The spin polarized electrons generated in GaAs by circularly polarized light were dragged by an electric field and the AHE was observed without an external magnetic field. As no magnetic field was applied, the observed photo-induced AHE was the pure AHE. The experiments also detected photogenerated spin current and spin relaxation electrically, based on the measurements of the photo-induced anomalous Hall voltage (VAH) at room temperature as well as at low temperatures. It was found that the effect strongly depends on the applied electric field and excited photon energy. The AHE was also found to be enhanced by moderately increasing the doping density or decreasing the temperature. The results are discussed in comparison with a quantitative evaluation of the Dyakonov and Perel spin relaxation frequencies of the photogenerated electrons in GaAs. A good agreement between theory and experiment was obtained. Three spin transport regimes were considered in relation to photo-induced AHE measurements with moderately-doped samples, namely, diffusive, drift-diffusion crossover and drift. Of them, spin transport in the diffusive and drift-diffusion crossover regimes were studied in more details and E ~ and D0 were estimated in the NDG regime. The electrically obtained value of D0 was found to be 1.74 ƒÊm, a factor of 0.87 lower than that reported in the literature of optical measurements. A time-resolved pump-probe polarization investigation was performed to measure the spin polarization for the samples. The spin polarization of conduction band electrons, as measured using probe pulses with the same and opposite circular polarizations, was studied via the dependences of pump-probe delay, temperature, doping density as well as of the excitation photon energy. For a comparison with the experimental data, a calculation for the AHE was performed using the measured degree of spin polarization. A band energy structure calculation for Si-doped GaAs was performed by norm-conserving pseudopotential and Green function methods. The results showed that simultaneously accounting for the external biased electric-field and delocalization of the spin-polarized wave-functions by anharmonic electron-phonon interactions can explain the electric field- and doping-dependent spin current and hence the observed VAH. The theoretically obtained results generally agreed with the experimental results